Fatigue Modeling for Elastic Materials With Statistically Distributed Defects

The paper is devoted to formulation and analysis of a new model of structural fatigue that is a direct extension of the model of contact fatigue developed by Kudish (2000, STLE Tribol. Trans., 43, pp. 711–721). The model is different from other published models of structural fatigue (Collins, J. A., 1993, Failure of Materials and Mechanical Design: Analysis, Prediction, Prevention, 2nd ed., Wiley, New York) in a number of aspects such as statistical approach to material defects, stress analysis, etc. The model is based on fracture mechanics and fatigue crack propagation. The model takes into account local stress distribution, initial statistical distribution of defects versus their size, crack location, and orientation, and material fatigue resistance parameters. The assumptions used for the new model derivation are stated clearly and their validity is discussed. The model considers the kinetics of crack distribution by taking into account the fact that the crack distribution varies with the number of applied loading cycles due to crack growth. A qualitative and quantitative parametric analysis of the model is performed. Some analytical formulas for fatigue life as a function of the initial defect distribution, material fatigue resistance, and stress state are obtained. Examples of application of the model to predicting fatigue of beam bending and torsion and contact fatigue for tapered bearings is presented.